Question

Four tomatoes and eight avocados cost $10. Six tomatoes and fourteen avocados cost $17.

Part A: Determine the price for a single tomato and a single avocado.


Part B: Analyze your results to determine if they are feasible.

Answer 1

(a)

A single avocado costs $1

A single tomato costs $0.5

(b)

An avocado costs twice as much as a tomato

Explanation:

Represent the tomatoes with T and the avocados with A.

So, we have:

`4T + 8A = 10` --- (1)

`6T + 14A = 17` --- (2)

Solving (a): The price of each

Multiply (1) by 1.5

`1.5(4T + 8A = 10)`

`6T + 12A = 15` --- (3)

Subtract (3) from (2)

`(6T + 14A = 17) - (6T + 12A = 15)`

`6T - 6T + 14A - 12A = 17 - 15`

`14A - 12A = 17 - 15`

`2A = 2`

Divide both sides by 2

`A = 1`

Substitute 1 for A in (1)

`4T + 8A = 10`

`4T + 8(1) = 10`

`4T + 8 = 10`

Make 4T the subject

`4T = 10 - 8`

`4T = 2`

Divide both sides by 4

`T = (2)/(4)`

`T = 0.5`

Solving (b): Analysis

In (a), we have:

`T = 0.5`

`A = 1`

We can say that an avocado costs twice as much as a tomato